There are two approaches to the analysis of complex sample data in Mplus. The first approach is to compute standard errors and chi-square tests of model fit taking into account complex sampling features. These include stratification, sampling weights, and clustering. Standard error computations use a sandwich estimator. This is referred to as TYPE=COMPLEX in Mplus. For this approach, observed dependent variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. When observed dependent variables are all continuous, Mplus has one estimator choice: maximum likelihood with robust standard errors and chi-square (MLR). When at least one observed dependent variable is binary or ordered categorical, Mplus has five estimator choices: weighted least squares (WLS), robust weighted least squares (WLSM, WLSMV), maximum likelihood with robust standard errors and chi-square (MLR), and unweighted least squares (ULS). When at least one observed dependent variable is censored, unordered categorical, or a count, Mplus has four estimator choices: weighted least squares (WLS), robust weighted least squares (WLSM, WLSMV), and maximum likelihood with robust standard errors and chi-square (MLR).

The second approach is to specify a model for each level of the multilevel data, commonly referred to as multilevel modeling. This is referred to as TYPE=TWOLEVEL in Mplus. The multilevel extension of the full Mplus modeling framework allows random intercepts and random slopes that vary across clusters in hierarchical data. These random effects can be specified for any of the relationships of the full model. Random effects representing across-cluster variation in intercepts and slopes or individual differences in growth can be combined with factors measured by multiple indicators on both the individual and cluster levels. In line with SEM, regressions among random effects, among factors, and between random effects and factors are allowed. For this approach, observed dependent variables can be continuous, binary, ordered categorical (ordinal), or combinations of these variable types. When observed dependent variables are all continuous, Mplus has four estimator choices: Muthen’s limited information estimator (MUML), maximum likelihood (ML), and maximum likelihood with robust standard errors and chi-square (MLR, MLF). When at least one observed dependent variable is binary or ordered categorical, Mplus has three estimator choices: maximum likelihood (ML) and maximum likelihood with robust standard errors and chi-square (MLR, MLF).

Besides controlling for clustering, TYPE=TWOLEVEL allows the use of sampling weights and stratification in the estimation of parameters, standard errors, and chi-square tests of model fit. With sampling weights, parameters are estimated by maximizing a weighted loglikelihood function.